189 citations · 1.9k across the 148 of their papers we have counts for
7 papers · 2 filters
A note on Ito's formula for discrete-time quantum walk
Norio Konno
We present an Ito's formula for the one-dimensional discrete-time quantum walk and give some examples including a Tanaka's formula by using the formula. Moreover we discuss integra…
Time averaged distribution of a discrete-time quantum walk on the path
Yusuke Ide, Norio Konno, Etsuo Segawa
The discrete time quantum walk which is a quantum counterpart of random walk plays important roles in the theory of quantum information theory. In the present paper, we focus on di…
The Heun differential equation and the Gauss differential equation related to quantum walks
Norio Konno, Takuya Machida, Tohru Wakasa
The limit theorems of discrete- and continuous-time quantum walks on the line have been intensively studied. We show a relation among limit distributions of quantum walks, Heun dif…
Limit measures of inhomogeneous discrete-time quantum walks in one dimension
Norio Konno, Tomasz Luczak, Etsuo Segawa
We treat three types of measures of the quantum walk (QW) with the spatial perturbation at the origin, which was introduced by [1]: time averaged limit measure, weak limit measure,…
Return probability of one-dimensional discrete-time quantum walks with final-time dependence
Yusuke Ide, Norio Konno, Takuya Machida +1
We analyze final-time dependent discrete-time quantum walks in one dimension. We compute asymptotics of the return probability of the quantum walk by a path counting approach. More…
On the relation between quantum walks and zeta functions
Norio Konno, Iwao Sato
We present an explicit formula for the characteristic polynomial of the transition matrix of the discrete-time quantum walk on a graph via the second weighted zeta function. As app…
Sojourn times of the Hadamard walk in one dimension
Norio Konno
The Hadamard walk is a typical model of the discrete-time quantum walk. We investigate sojourn times of the Hadamard walk on a line by a path counting method.